Molecular topology of dendrimers

The circuit polynomial of the restricted rooted product G(Γ) of graphs with a bipartite core G

“…Another interesting example of rooted product is the family of dendrimers D k (k 0) (see [14,15,20,28]), defined as follows: D 0 = K 1 , D 1 = G, D 2 is the rooted product of G and H, in which some attachments of H are not made, i.e., H need not be attached to all nodes of G. In general, D s+1 (s 1) is constructed from D s ; and the number of copies attached to D s obeys some fixed generation law. The dendrimers, in particular, imitate molecular structures, bearing the same name [22,[1][2][3][4]32,14,15,20,28]. They are of practical significance [22,[1][2][3][4]32].…”

“…Let (a copy of) H invariably make d + 1 (d < p(H )) attachments inside a dendrimer D. Of this amount, 1 attachment is to hold the root of H itself while the other d are to hold the roots of all its incident neighbors in D. The number d is called a progressive degree of H (cf. [15]). A dendrimer is said to be homogeneous if all its monodendrons are equivalent and all prescribed attachments within it are made (cf.…”

Vertex-Eccentricity Descriptors in Dendrimers

“…Dendrimers are highly ordered hyper-branched molecular structures [10][11][12] reaching the nano-dimensions. The end-groups (the pendant groups reaching the outer periphery) can be functionalized, thus modifying their physico-chemical or biological properties.…”

The study of an infinite class of dendrimer nanostars by topological index approaches

“…In an exact phrase, dendrimers are hyperbranched macromolecules, showing a rigorous, aesthetically appealing architecture. The nanostar dendrimer is part of a new group of macromolecules having great applications but first the structure must be understood [1].…”